Model selection for integrated pest management with stochasticity. (7th April 2018)

• Record Type: Journal Article
• Authors: Akman, Olcay; Comar, Timothy D.; Hrozencik, Daniel
• Is Part Of: Journal of theoretical biology. Volume 442(2018)
• Page Start: 110
• Page End: 122
• Publication Date: 2018-04-07
• Subjects: Integrated pest management -- Birth pulse -- Mixture model -- Impulsive differential equations -- Permanence -- Stochasticity; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2017.12.005
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: Deterministic and stochastic models for integrated pest management, including stage structure and birth pulse for the pest species, are presented. Model components create flexibility in modeling the impacts of random environmental changes. Conditions under which the deterministic system remains permanent are established. An optimal value of the mixing parameter of the stochastic model is determined and shown to be robust. Numerical simulations show that permanence can be maintained in the stochastic model. Abstract: In Song and Xiang (2006), an integrated pest management model with periodically varying climatic conditions was introduced. In order to address a wider range of environmental effects, the authors here have embarked upon a series of studies resulting in a more flexible modeling approach. In Akman et al. (2013), the impact of randomly changing environmental conditions is examined by incorporating stochasticity into the birth pulse of the prey species. In Akman et al. (2014), the authors introduce a class of models via a mixture of two birth-pulse terms and determined conditions for the global and local asymptotic stability of the pest eradication solution. With this work, the authors unify the stochastic and mixture model components to create further flexibility in modeling the impacts of random environmental changes on an integrated pest management system. In particular, we first determine the conditions under which solutions of our deterministic mixture model are permanent. We then analyze the stochastic model to find the optimal value of the mixing parameter that minimizes the variance in the efficacy of the pesticide. Additionally, we perform a sensitivity analysis to show that the corresponding pesticide efficacy determined by this optimization technique is indeed robust. Through numerical simulations we show that permanence can be preserved in our stochastic model. Our study of the stochastic version of the model indicates that our results on the deterministic model provide informative conclusions about the behavior of the stochastic model.